Light Scanning Photomacrography (LSP), also known as Scanning Light Photomacrography (SLP) or Deep-Field Photomacrography, is a photographic film technique that allows for high magnification light imaging with exceptional depth of field (DOF). This method overcomes the limitations of conventional macro photography, which typically only keeps a portion of the subject in acceptable focus at high magnifications. == Historical background == The principles of LSP were first documented in the early 1960s by Dan McLachlan Jr., who highlighted its capability for extreme focal depth in microscopy and in 1968 patented the process. The technique was revived and further developed in the 1980s by photographers such as Darwin Dale and Nile Root, a faculty member at the Rochester Institute of Technology. In the early 1990s, William Sharp and Charles Kazilek, both researchers at Arizona State University, also published articles describing their technique and system setup for capturing SLP images. == Predecessor to stack image photography == Light Scanning Photomacrography offered a powerful analog tool for high-detail imaging in the age of film photography. It provided a comprehensive depth of field, making it invaluable in scientific and biomedical photography. As technology and techniques continue to evolve, LSP has been replaced by digital image focus stacking. This technique uses a collection of images captured in series at different focal depths, which are then processed using computer software to create a single image with a greater focus depth than any single image. == LSP technique and results == LSP involves the use of a thin plane of light that scans across the subject, which is mounted on a stage moving perpendicular to the film plane. The technique utilizes traditional optics and is governed by the physical laws of depth of field. By moving the subject through a narrow band of illumination, the entire subject can be recorded in sharp focus from the nearest details to the farthest ones. This analog process produces sharp and detailed images by slowly recording the image on film as the specimen passes through the sheet of light that is thinner than the effective DOF. Because the image is captured at the same relative distance from the camera lens, the resulting images are axonometric rather than perspective projection, which is what the human eye sees and is typically captured by a film camera. Because all parts of an LSP image are captured at the same distance from the lens, relative measurements can be taken from an LSP photograph and can be used for comparison. == Equipment and setup == A typical LSP setup includes: A stage that can move the subject perpendicular to the film plane. Light sources, in some cases modified projectors, are used to project a thin plane of light. A camera mounted on a stable stand such as a tabletop copy stand. In 1991, Sharp and Kazilek described their SLP system that used three Kodak Ektagraphic slide projectors with zoom lenses to create a thin plane of light. The projectors each had a slide mount with two razor blades placed edge-to-edge to create a thin slit for the light to pass through. The image was captured using a Nikon FE-2 SLR camera mounted above the specimen. Kodachrome 25 slide film was used to record the image and to minimize film grain size and maximize image sharpness == Commercial systems == A commercial SLP instrument was produced by the Irvine Optical Corp. Their DYNAPHOT system was based on a photomacroscope and could capture images on 4x5 film. The instrument came with two or three illumination sources and a motorized specimen stage. The system advertised a 2X – 40X magnification range and the ability to capture images in black and white and color. Other systems have been developed by Nile Root and Theodore Clarke and reported higher magnification (up to 100X). == LSP process == Alignment and Focusing: The light sources are aligned and focused to project a thin, consistent plane of light across the subject. Stage Movement: The subject stage moves at a controlled speed, scanning through the plane of light. Image Capture: The camera shutter is set to a long exposure or can be opened and closed manually. As the subject moves through the illuminated plane, it is recorded on the film. This process is very much like painting an image onto the film using photons instead of paint. == Applications == LSP was particularly useful in biomedical photography, where it was used to document magnified subjects with increased depth of field over traditional macro and micro photography. It has been employed to capture detailed images of biological specimens, such as imaging small insects and their parts. SLP has been used to document shell collections for scientific documentation and research. Other applications include forensic science, mineralogy, and the imaging of fractured surfaces and parts == Advantages and challenges of LSP imaging == === Advantages === Exceptional depth of field: Subjects are rendered in sharp focus throughout. High magnification: Detailed images at significant magnification without sacrificing DOF. Analog precision: Provides a non-digital solution with accurate image representation. Versatility: Can be used for a range of subject sizes, from macro to non-macro scales. === Challenges === Technical complexity: Requires precise setup and alignment. Exposure time: Typically requires long exposure times due to the scanning process. Contrast control: The highly directional lighting can create harsh shadows and high contrast, which may need to be managed. Digital competition: Focus stacking has largely replaced LSP in the digital era due to convenience and flexibility. == DIY contributions == Enthusiasts and researchers have contributed to the development and accessibility of LSP by creating and sharing DIY guides. These contributions have enabled others to build their own LSP systems using readily available materials and components. Nile Root's publications provide detailed instructions and recommendations for constructing an LSP setup. These DIY systems have allowed a wider audience to explore and utilize the benefits of LSP imaging in various fields.
List of video editing software
The following is a list of video editing software. The criterion for inclusion in this list is the ability to perform non-linear video editing. Most modern transcoding software supports transcoding a portion of a video clip, which would count as cropping and trimming. However, items in this article have one of the following conditions: Can perform other non-linear video editing function such as montage or compositing Can do the trimming or cropping without transcoding == Free (libre) or open-source == The software listed in this section is either free software or open source, and may or may not be commercial. === Active and stable === === Inactive === == Proprietary (non-commercial) == The software listed in this section is proprietary, and freeware or freemium. === Active === === Discontinued === == Proprietary (commercial) == The software listed in this section is proprietary and commercial. === Active === === Discontinued ===
AlphaGo Zero
AlphaGo Zero is a version of DeepMind's Go software AlphaGo. AlphaGo's team published an article in Nature in October 2017 introducing AlphaGo Zero, a version created without using data from human games, and stronger than any previous version. By playing games against itself, AlphaGo Zero: surpassed the strength of AlphaGo Lee in three days by winning 100 games to 0; reached the level of AlphaGo Master in 21 days; and exceeded all previous versions in 40 days. Training artificial intelligence (AI) without datasets derived from human experts has significant implications for the development of AI with superhuman skills, as expert data is "often expensive, unreliable, or simply unavailable." Demis Hassabis, the co-founder and CEO of DeepMind, said that AlphaGo Zero was so powerful because it was "no longer constrained by the limits of human knowledge". Furthermore, AlphaGo Zero performed better than standard deep reinforcement learning models (such as Deep Q-Network implementations) due to its integration of Monte Carlo tree search. David Silver, one of the first authors of DeepMind's papers published in Nature on AlphaGo, said that it is possible to have generalized AI algorithms by removing the need to learn from humans. Google later developed AlphaZero, a generalized version of AlphaGo Zero that could play chess and shōgi in addition to Go. In December 2017, AlphaZero beat the 3-day version of AlphaGo Zero by winning 60 games to 40, and with 8 hours of training it outperformed AlphaGo Lee on an Elo scale. AlphaZero also defeated a top chess program (Stockfish) and a top Shōgi program (Elmo). == Architecture == The network in AlphaGo Zero is a ResNet with two heads. The stem of the network takes as input a 17x19x19 tensor representation of the Go board. 8 channels are the positions of the current player's stones from the last eight time steps. (1 if there is a stone, 0 otherwise. If the time step go before the beginning of the game, then 0 in all positions.) 8 channels are the positions of the other player's stones from the last eight time steps. 1 channel is all 1 if black is to move, and 0 otherwise. The body is a ResNet with either 20 or 40 residual blocks and 256 channels. There are two heads, a policy head and a value head. Policy head outputs a logit array of size 19 × 19 + 1 {\displaystyle 19\times 19+1} , representing the logit of making a move in one of the points, plus the logit of passing. Value head outputs a number in the range ( − 1 , + 1 ) {\displaystyle (-1,+1)} , representing the expected score for the current player. -1 represents current player losing, and +1 winning. == Training == AlphaGo Zero's neural network was trained using TensorFlow, with 64 GPU workers and 19 CPU parameter servers. Only four TPUs were used for inference. The neural network initially knew nothing about Go beyond the rules. Unlike earlier versions of AlphaGo, Zero only perceived the board's stones, rather than having some rare human-programmed edge cases to help recognize unusual Go board positions. The AI engaged in reinforcement learning, playing against itself until it could anticipate its own moves and how those moves would affect the game's outcome. In the first three days AlphaGo Zero played 4.9 million games against itself in quick succession. It appeared to develop the skills required to beat top humans within just a few days, whereas the earlier AlphaGo took months of training to achieve the same level. According to Epoch.ai, training cost 3e23 FLOPs. For comparison, the researchers also trained a version of AlphaGo Zero using human games, AlphaGo Master, and found that it learned more quickly, but actually performed more poorly in the long run. DeepMind submitted its initial findings in a paper to Nature in April 2017, which was then published in October 2017. == Hardware cost == The hardware cost for a single AlphaGo Zero system in 2017, including the four TPUs, has been quoted as around $25 million. == Applications == According to Hassabis, AlphaGo's algorithms are likely to be of the most benefit to domains that require an intelligent search through an enormous space of possibilities, such as protein folding (see AlphaFold) or accurately simulating chemical reactions. AlphaGo's techniques are probably less useful in domains that are difficult to simulate, such as learning how to drive a car. DeepMind stated in October 2017 that it had already started active work on attempting to use AlphaGo Zero technology for protein folding, and stated it would soon publish new findings. == Reception == AlphaGo Zero was widely regarded as a significant advance, even when compared with its groundbreaking predecessor, AlphaGo. Oren Etzioni of the Allen Institute for Artificial Intelligence called AlphaGo Zero "a very impressive technical result" in "both their ability to do it—and their ability to train the system in 40 days, on four TPUs". The Guardian called it a "major breakthrough for artificial intelligence", citing Eleni Vasilaki of Sheffield University and Tom Mitchell of Carnegie Mellon University, who called it an impressive feat and an “outstanding engineering accomplishment" respectively. Mark Pesce of the University of Sydney called AlphaGo Zero "a big technological advance" taking us into "undiscovered territory". Gary Marcus, a psychologist at New York University, has cautioned that for all we know, AlphaGo may contain "implicit knowledge that the programmers have about how to construct machines to play problems like Go" and will need to be tested in other domains before being sure that its base architecture is effective at much more than playing Go. In contrast, DeepMind is "confident that this approach is generalisable to a large number of domains". In response to the reports, South Korean Go professional Lee Sedol said, "The previous version of AlphaGo wasn’t perfect, and I believe that’s why AlphaGo Zero was made." On the potential for AlphaGo's development, Lee said he will have to wait and see but also said it will affect young Go players. Mok Jin-seok, who directs the South Korean national Go team, said the Go world has already been imitating the playing styles of previous versions of AlphaGo and creating new ideas from them, and he is hopeful that new ideas will come out from AlphaGo Zero. Mok also added that general trends in the Go world are now being influenced by AlphaGo's playing style. "At first, it was hard to understand and I almost felt like I was playing against an alien. However, having had a great amount of experience, I’ve become used to it," Mok said. "We are now past the point where we debate the gap between the capability of AlphaGo and humans. It’s now between computers." Mok has reportedly already begun analyzing the playing style of AlphaGo Zero along with players from the national team. "Though having watched only a few matches, we received the impression that AlphaGo Zero plays more like a human than its predecessors," Mok said. Chinese Go professional Ke Jie commented on the remarkable accomplishments of the new program: "A pure self-learning AlphaGo is the strongest. Humans seem redundant in front of its self-improvement." == Comparison with predecessors == == AlphaZero == On 5 December 2017, DeepMind team released a preprint on arXiv, introducing AlphaZero, a program using generalized AlphaGo Zero's approach, which achieved within 24 hours a superhuman level of play in chess, shogi, and Go, defeating world-champion programs, Stockfish, Elmo, and 3-day version of AlphaGo Zero in each case. AlphaZero (AZ) is a more generalized variant of the AlphaGo Zero (AGZ) algorithm, and is able to play shogi and chess as well as Go. Differences between AZ and AGZ include: AZ has hard-coded rules for setting search hyperparameters. The neural network is now updated continually. Chess (unlike Go) can end in a tie; therefore AZ can take into account the possibility of a tie game. An open source program, Leela Zero, based on the ideas from the AlphaGo papers is available. It uses a GPU instead of the TPUs recent versions of AlphaGo rely on.
Hallin's spheres
Hallin's spheres is a theory of news reporting and its rhetorical framing posited by journalism historian Daniel C. Hallin in his 1986 book The Uncensored War to explain the news coverage of the Vietnam War. Hallin divides the world of political discourse into three concentric spheres: consensus, legitimate controversy, and deviance. In the sphere of consensus, journalists assume everyone agrees. The sphere of legitimate controversy includes the standard political debates, and journalists are expected to remain neutral. The sphere of deviance falls outside the bounds of legitimate debate, and journalists can ignore it. These boundaries shift, as public opinion shifts. Hallin's spheres, which deals with the media, are similar to the Overton window, which deals with public opinion generally, and posits a sliding scale of public opinion on any given issue ranging from conventional wisdom to unacceptable. Hallin used the concept of framing to describe the presentation and reception of issues in public. For example, framing the use of drugs as criminal activity can encourage the public to consider that behavior anti-social. Hallin's work was later referred to in the controversial formulation of the concept of an opinion corridor, in which the range of acceptable public opinion narrows, and opinion outside that corridor moves from legitimate controversy into deviance. == Description == === Sphere of consensus === This sphere contains those topics on which there is widespread agreement, or at least the perception thereof. Within the sphere of consensus, "journalists feel free to invoke a generalized 'we' and to take for granted shared values and shared assumptions". Examples include such things as motherhood and apple pie. For topics in this sphere, journalists feel free to be advocating cheerleaders without having to be neutral or present any opposing view point and be disinterested observers." === Sphere of legitimate controversy === For topics in this sphere rational and informed people hold differing views within limited range. These topics are therefore the most important to cover, and also ones upon which journalists are seemingly obliged to remain disinterested reporters, rather than advocating for or against a particular view. Schudson notes that Hallin, in his influential study of the US media during the Vietnam War, argues that journalism's commitment to objectivity has always been compartmentalized. That is, within a certain sphere—the sphere of legitimate controversy—journalists seek conscientiously to be balanced and objective. The work of Walter Williams professor at the University of Missouri, Rod Petersen, advanced the idea that priming—controlling the narratives that media covers—can be the tool that media use to get deviant news subjects into the legitimate controversial circles of new coverage. === Sphere of deviance === Topics in this sphere are rejected by journalists as being unworthy of general consideration. Such views are perceived as being out of hand, unfounded, taboo, or of such minor consequence that they are not newsworthy. Hallin argues that in the sphere of deviance, "journalists also depart from standard norms of objective reporting and feel authorized to treat as marginal, laughable, dangerous". They either avoid mentioning or ridicule the controversial subject as outside the bounds of acceptable controversy; and they censor the individuals and groups who are associated with it. A simple example: a person claiming that aliens are manipulating college basketball scores might have difficulty finding sports media coverage for such a claim. A more political example: the US media regulator FCC's "Fairness Doctrine" aimed at radio stations, advocated balance between right and left political news and opinions, yet specified that broadcasters did not have to reserve any space or time for Communist viewpoints. == Uses of the terms == Craig Watkins (2001, pp. 92–94) makes use of the Hallin's spheres in a paper examining ABC, CBS, and NBC television network television news coverage of the Million Man March, a demonstration that took place in Washington, D.C., on October 16, 1995. Watkins analyzes the dominant framing practices—problem definition, rhetorical devices, use of sources, and images—employed by journalists to make sense of this particular expression of political protest. He argues that Hallin's three spheres are a way for media framing practices to develop specific reportorial contexts, and each sphere develops its own distinct style of news reporting resources by different rhetorical tropes and discourses. Piers Robinson (2001, p. 536) uses the concept in relation to debates that have emerged over the extent to which the mass media serves elite interests or, alternatively, plays a powerful role in shaping political outcomes. His article reviews Hallin's spheres as an example of media-state relations, that highlights theoretical and empirical shortcomings in the 'manufacturing consent' thesis (Chomsky, McChesney). Robinson argues that a more nuanced and bi-directional understanding is needed of the direction of influence between media and the state that builds upon, rather than rejecting, existing theoretical accounts. Hallin's theory assumed a relatively homogenized media environment, where most producers were trying to reach most consumers. A more fractured media landscape can challenge this assumption because different audiences may place topics in different spheres, a concept related to the filter bubble, which posits that many members of the public choose to limit their media consumption to the areas of consensus and deviance that they personally prefer.
Library classification
A library classification is a system used within a library to organize materials, including books, sound and video recordings, electronic materials, etc., both on shelves and in catalogs and indexes. Each item is typically assigned a call number, which identifies the location of the item within the system. Materials can be arranged by many different factors, typically in either a hierarchical tree structure based on the subject or using a faceted classification system, which allows the assignment of multiple classifications to an object, enabling the classifications to be ordered in many ways. == Description == Library classification is an important and crucial aspect in library and information science. It is distinct from scientific classification in that it has as its goal to provide a useful ordering of documents rather than a theoretical organization of knowledge. Although it has the practical purpose of creating a physical ordering of documents, it does generally attempt to adhere to accepted scientific knowledge. Library classification helps to accommodate all the newly published literature in an already created order of arrangement in a filial sequence. Library classification can be defined as the arrangement of books on shelves, or description of them, in the manner which is most useful to those who read with the ultimate aim of grouping similar things together. Library classification is meant to achieve these four purposes: ordering the fields of knowledge in a systematic way, bring related items together in the most helpful sequence, provide orderly access on the shelf, and provide a location for an item on the shelf. Library classification is distinct from the application of subject headings in that classification organizes knowledge into a systematic order, while subject headings provide access to intellectual materials through vocabulary terms that may or may not be organized as a knowledge system. The characteristics that a bibliographic classification demands for the sake of reaching these purposes are: a useful sequence of subjects at all levels, a concise memorable notation, and a host of techniques and devices of number synthesis. == History == Library classifications were preceded by classifications used by bibliographers such as Conrad Gessner. The earliest library classification schemes organized books in broad subject categories. The earliest known library classification scheme is the Pinakes by Callimachus, a scholar at the Library of Alexandria during the third century BC. During the Renaissance and Reformation era, "Libraries were organized according to the whims or knowledge of individuals in charge." This changed the format in which various materials were classified. Some collections were classified by language and others by how they were printed. After the printing revolution in the sixteenth century, the increase in available printed materials made such broad classification unworkable, and more granular classifications for library materials had to be developed in the nineteenth century. In 1627 Gabriel Naudé published a book called Advice on Establishing a Library. At the time, he was working in the private library of Président à mortier Henri de Mesmes II. Mesmes had around 8,000 printed books and many more Greek, Latin and French written manuscripts. Although it was a private library, scholars with references could access it. The purpose of Advice on Establishing a Library was to identify rules for private book collectors to organize their collections in a more orderly way to increase the collection's usefulness and beauty. Naudé developed a classification system based on seven different classes: theology, medicine, jurisprudence, history, philosophy, mathematics, and the humanities. These seven classes would later be increased to twelve. Advice on Establishing a Library was about a private library, but within the same book, Naudé encouraged the idea of public libraries open to all people regardless of their ability to pay for access to the collection. One of the most famous libraries that Naudé helped improve was the Bibliothèque Mazarine in Paris. Naudé spent ten years there as a librarian. Because of Naudé's strong belief in free access to libraries to all people, the Bibliothèque Mazarine became the first public library in France around 1644. Although libraries created order within their collections from as early as the fifth century BC, the Paris Bookseller's classification, developed in 1842 by Jacques Charles Brunet, is generally seen as the first of the modern book classifications. Brunet provided five major classes: theology, jurisprudence, sciences and arts, belles-lettres, and history. Classification can now be seen as a provider of subject access to information in a networked environment. == Types == There are many standard systems of library classification in use, and many more have been proposed over the years. However, in general, classification systems can be divided into three types depending on how they are used: === Universal schemes === Covers all subjects, e.g. the Dewey Decimal Classification (DDC), Universal Decimal Classification (UDC), and Colon Classification (CC). === Specific classification schemes === Covers particular subjects or types of materials, e.g. Iconclass (art), British Catalogue of Music Classification, and Dickinson classification (music), or the NLM Classification (medicine). === National schemes === Specially created for certain countries, e.g. Swedish library classification system, SAB (Sveriges Allmänna Biblioteksförening). The Library of Congress Classification was designed around the collection of the US Library of Congress and has an American, European, and Christian bias. Nevertheless, it is used widely in large academic and research libraries. In terms of functionality, classification systems are often described as: === Enumerative === Subject headings are listed alphabetically, with numbers assigned to each heading in alphabetical order. === Hierarchical === Subjects are divided hierarchically, from most general to most specific. === Faceted/analytico-synthetic === Subjects are divided into mutually exclusive orthogonal facets. There are few completely enumerative systems or faceted systems; most systems are a blend but favouring one type or the other. The most common classification systems, LCC and DDC, are essentially enumerative, though with some hierarchical and faceted elements (more so for DDC), especially at the broadest and most general level. The first true faceted system was the colon classification of S. R. Ranganathan. == Methods or systems == Classification types denote the classification or categorization according to the form or characteristics or qualities of a classification scheme or schemes. Method and system has similar meaning. Method or methods or system means the classification schemes like Dewey Decimal Classification or Universal Decimal Classification. The types of classification is for identifying and understanding or education or research purposes while classification method means those classification schemes like DDC, UDC. === English language universal classification systems === The most common systems in English-speaking countries are: Dewey Decimal Classification (DDC) Library of Congress Classification (LCC) Universal Decimal Classification (UDC) Other systems include: Book Industry Standards and Communications (BISAC), originally developed for use by U.S. booksellers, has become increasingly popular in libraries. Bliss bibliographic classification used in some British libraries Colon classification (CC) Garside classification used in most libraries of University College London Gladstone Library Classification, devised by W.E. Gladstone and used exclusively at Gladstone's Library Harvard-Yenching Classification, an English classification system for Chinese language materials === Non-English universal classification systems === German Regensburger Verbundklassifikation (RVK) A system of book classification for Chinese libraries (Liu's Classification) library classification for user New Classification Scheme for Chinese Libraries Nippon Decimal Classification (NDC) Chinese Library Classification (CLC) Korean Decimal Classification (KDC) Russian Library-Bibliographical Classification (BBK) Swedish library classification system (SAB) === Universal classification systems that rely on synthesis (faceted systems) === Bliss bibliographic classification Colon classification Cutter Expansive Classification Universal Decimal Classification Newer classification systems tend to use the principle of synthesis (combining codes from different lists to represent the different attributes of a work) heavily, which is comparatively lacking in LC or DDC. == Practice == Library classification is associated with library (descriptive) cataloging under the rubric of cataloging and classification, sometimes grouped together as technical serv
DexNet
Dex-net is a robotic. It uses a Grasp Quality Convolutional Neural Network to learn how to grasp unusually shaped objects. == History == Dex-net was developed by University of California, Berkeley professor Ken Goldberg and graduate student Jeff Mahler. == Design == Dex-net includes a high-resolution 3-D sensor and two arms, each controlled by a different neural network. One arm is equipped with a conventional robot gripper and another with a suction system. The robot’s software scans an object and then asks both neural networks to decide, on the fly, whether to grab or suck a particular object. It runs on an off-the-shelf industrial machine made by Swiss robotics company ABB. The software learns by attempting to pick up objects in a virtual environment. Dex-Net can generalize from an object it has seen before to a new one. The robot can "nudge" such virtual objects to examine if it is unsure how to grasp them. The trial data set was 6.7 million point clouds, grasps and analytic grasp metrics generated from thousands of 3D models. Grasps are defined as a gripper's planar position, angle and depth relative to an RGB-D sensor. == Mean picks per hour == A metric called mean picks per hour (MPPH) is calculated by multiplying the average time per pick and the average probability of success for a specific set of objects. The new metric allows labs working on picking robots to compare their results. Humans are capable of between 400 and 600 MPPH. In a contest organized by Amazon recently, the best robots were capable of between 70 and 95. Dex-net has achieved 200 to 300.
AlphaGeometry
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language model (LLM) and a rule-based symbolic engine (Deductive Database Arithmetic Reasoning). It was developed by DeepMind, a subsidiary of Google. The program solved 25 geometry problems out of 30 from the International Mathematical Olympiad (IMO) under competition time limits—a performance almost as good as the average human gold medallist. For comparison, the previous AI program, called Wu's method, managed to solve only 10 problems. DeepMind published a paper about AlphaGeometry in the peer-reviewed journal Nature on 17 January 2024. AlphaGeometry was featured in MIT Technology Review on the same day. Traditional geometry programs are symbolic engines that rely exclusively on human-coded rules to generate rigorous proofs, which makes them lack flexibility in unusual situations. AlphaGeometry combines such a symbolic engine with a specialized large language model trained on synthetic data of geometrical proofs. When the symbolic engine doesn't manage to find a formal and rigorous proof on its own, it solicits the large language model, which suggests a geometrical construct to move forward. However, it is unclear how applicable this method is to other domains of mathematics or reasoning, because symbolic engines rely on domain-specific rules and because of the need for synthetic data. == AlphaGeometry 2 == AlphaGeometry 2 is an improved version of AlphaGeometry, published on February 5, 2025. They added more features to the representation language to describe more geometry problems that involve movements of objects, and problems containing linear equations of angles, ratios, and distances. They targeted IMO geometry questions from 2000 to 2024. The expanded representation language allowed them to cover 88% of the questions. It uses Gemini finetuned on a synthetically generated dataset of problems and solutions in the representation language. The model is used for making auxiliary constructions like lines and points, to help the tree search. It is also used for autoformalization, i.e. converting a problem in English to a problem in the representation language.